Question

Solve the equation x2-y2=27 and x + y=3

Answer 1

$x^{2} - y^{2} =27...............1 \\ x+y=3...............2 \\ from eq. 2 \\ x=3-y$
putting the value of x in 1
$(3-y)^{2} + y^{2} =27 \\ 9+ y^{2} -6y- y^{2} =27 \\ -6y=18 \\ y=-3$
putting the value of y in 2
$x-3=3 \\ x=6 ans..$

Answer 2

we know that x2 - y2= (x+y)(x-y)
therefore our equation becomes (x+y)(x-y) = 27

we know that x+y = 3............................................................(1)
therefore    3(x-y)=27
x - y= 9................................................................................(2)

from (1) and (2).....we get  x=  6
and                                 y= (-3)